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# A company decreased the price of its main product by 50%

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Senior Manager
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A company decreased the price of its main product by 50% [#permalink]

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19 Nov 2011, 12:14
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Difficulty:

25% (medium)

Question Stats:

66% (00:58) correct 34% (00:53) wrong based on 330 sessions

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A company decreased the price of its main product by 50%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product?

A. 0.5
B. 1.0
C. 1.5
D. 2.0
E. 4.0
[Reveal] Spoiler: OA

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Re: a company decreased the price [#permalink]

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19 Nov 2011, 12:33
1
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For the total revenue to remain the same when the price is halved, the number of products sold must double. Therefore increase in the number of products sold is 100%

=> The required ratio = 100%/50% = 2.0

Option (D)
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Kudos [?]: 642 [1], given: 20

Senior Manager
Status: D-Day is on February 10th. and I am not stressed
Affiliations: American Management association, American Association of financial accountants
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Re: a company decreased the price [#permalink]

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19 Nov 2011, 14:37
Thank you good and easy one. for some reason i couldn't solve it, maybe i was stressed while taking the test. thanks again
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Re: a company decreased the price [#permalink]

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25 Mar 2012, 18:23
Price decreased so quantity must increase so the net effect of the 50% decrease and % increase in quantity must equal 1. And that is 200% increase. We are looking for the net % increase which is 100% increase and then take the ratio of that which is 100%/50% = 2.
D
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Re: A company decreased the price of its main product by 50% [#permalink]

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26 Mar 2012, 01:17
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Expert's post
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manalq8 wrote:
A company decreased the price of its main product by 50%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product?

A. 0.5
B. 1.0
C. 1.5
D. 2.0
E. 4.0

Nice explanation above by GyanOne.

One can also use plug-in method: consider the price of the product to be \$10 and the units sold at that price to be 1 --> revenue=\$10*1=\$10;

If we decrease the price by 50% from \$10 to \$5 then in order the revenue to remain the same 2 units must be sold which is 100% increase in sales (from 1 to 2).

Hence the ratio is 100%/50%=2.

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Re: A company decreased the price of its main product by 50% [#permalink]

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26 Mar 2012, 01:22
In such questions it is always easier to chose random values and solve the question.

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Re: A company decreased the price of its main product by 50% [#permalink]

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30 Dec 2012, 17:56
I used algebraical approach:
1) p1=p2
We know that p1q1=p2q2, let's apply here condition (1) ===> 2p2q1=p2q2. It means that 2q1=q2 or q2/q1=2
Manhattan CAT2 consider this question 700-800 which is not true.
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Re: A company decreased the price of its main product by 50% [#permalink]

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18 Nov 2013, 06:53
I'm confused. Can someone please help me understand why the ratio is 100/50? I get that the quantity halved and the price doubled. But I don't get why the final ratio is a 2 instead of a 1.

This is my reasoning with number:

Initial price= 100
Initial Units=100
x=new quantity

(100)(100)=10,000
(.5)(100)(x)=10,000
x=200 (new quantity)

Quantity percent increase=
(200-100/100)(100)=100% increase

Price decrease=
(100-50/50)=100% decrease

100/100=1

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Re: A company decreased the price of its main product by 50% [#permalink]

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18 Nov 2013, 06:57
1
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Expert's post
sarahmichalmoore wrote:
I'm confused. Can someone please help me understand why the ratio is 100/50? I get that the quantity halved and the price doubled. But I don't get why the final ratio is a 2 instead of a 1.

This is my reasoning with number:

Initial price= 100
Initial Units=100
x=new quantity

(100)(100)=10,000
(.5)(100)(x)=10,000
x=200 (new quantity)

Quantity percent increase=
(200-100/100)(100)=100% increase

Price decrease=
(100-50/50)=100% decrease

100/100=1

Is the price decrease from 100 to 50 a 100% decrease? It's 50% decrease: (100-50)/100=0.5.

Hope it's clear.
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Re: A company decreased the price of its main product by 50% [#permalink]

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18 Nov 2013, 13:14
Bunuel wrote:
sarahmichalmoore wrote:
I'm confused. Can someone please help me understand why the ratio is 100/50? I get that the quantity halved and the price doubled. But I don't get why the final ratio is a 2 instead of a 1.

This is my reasoning with number:

Initial price= 100
Initial Units=100
x=new quantity

(100)(100)=10,000
(.5)(100)(x)=10,000
x=200 (new quantity)

Quantity percent increase=
(200-100/100)(100)=100% increase

Price decrease=
(100-50/50)=100% decrease

100/100=1

Is the price decrease from 100 to 50 a 100% decrease? It's 50% decrease: (100-50)/100=0.5.

Hope it's clear.

yes it is. I made a very silly mistake. Thank you so much for clarifying!

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Re: A company decreased the price of its main product by 50% [#permalink]

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02 Jun 2014, 23:44
I also used an algebraic approach:

initial revenue: p * u = r (p = price; u = units; r= revenue)

now we have a decrease of 0.5 in p and an increase of x in u. r remains the same:

0.5p * (x*u) = r

now equalize:

0.5p * (x*u) = p * u ==> p/0.5p = x*u/u ==> 0.5p=x ==> x = 2 --> here's our ratio!

dunno if this it the right approach but it worked for me lol.

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A company decreased the price of its main product by 50% [#permalink]

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11 Aug 2015, 04:35
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Revenue = Price of product * Units sold

Old - \$1000 = \$100 * 10

New - \$1000 = \$50 * 20

Percent decrease of price of product = (100 - 50)/100 *100 = 50

Percent increase of units sold = (20 - 10)/10 *100 = 100

Required ratio = 100/50 = 2 (Answer choice D)
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Re: A company decreased the price of its main product by 50% [#permalink]

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01 Oct 2016, 04:50
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Re: A company decreased the price of its main product by 50% [#permalink]

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21 May 2017, 17:44
manalq8 wrote:
A company decreased the price of its main product by 50%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product?

A. 0.5
B. 1.0
C. 1.5
D. 2.0
E. 4.0

Smart numbers are the best solution to this problem.

If we start with PQ =4 and P =2 and Q =2, then we know that P becomes 1 and Q becomes 4. 4/2 = 1 = 100% growth for Q whereas we know that P decreased by 50%.

100%/50% = 2.0 or 200%, the ratio of the increase in quantity to the decrease in price (elasticity of the good).

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Re: A company decreased the price of its main product by 50%   [#permalink] 21 May 2017, 17:44
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